9.7 Graphs of Polar Equations
Discover the graphs of polar equations by using your graphing calculator to create the graphs of the
equations on the following pages. Sketch the graph on the axes provided.
Set the mode of your calculator to POL (POLAR) and your WINDOW
settings as above. In the "Y=" screen, the equation will be written as
"r = " and the independent variable will be θ. You may have to play
around with different window settings as you proceed and you may
wish to use ZOOM SQUARE to view the graphs appropriately.
Play with the TRACE button and advance around the graph
using the right and left arrow keys.
As you create each graph, determine the required θ to trace out the
graph just once. You will notice that for some graphs, the trace
repeats itself. You may wish to use the "tracing ball" to confirm this.
For instance, is the graph complete over the interval [0, 2π] or is it
complete over the interval [0, π] ? Record the domain of θ required
to complete each graph. Scroll to the left of the equal sign to call up
the tracing ball.
Limacon with inner loop
r = 1 + 2 cos θ
Cardioid
r = 3 + 3 sin θ
General Form: r = a ± b cos θ or r = a ± b sin θ
Dimpled Limacon
r = 3 - 2 cos θ
Rose curves
r = 2 sin 3θ
r = 4 cos 5θ
r = 3 sin 4θ
r = 5 cos 2θ
General Form:
r = a sin nθ or
r = a cos nθ
Circles
r = 6 cos θ
General Form:
r = 3 sin θ
r = a cos θ
or
r = a sin θ
Leminscates
r2 = 4 sin 2θ
General Form:
r2 = 9 cos 2θ
r2 = a2 sin 2θ
or
r2 = a2 cos 2θ
Use a table of values to do point by point plotting to
create a polar graph by hand.
r = 2 cos θ
r = 1 = 2 sin θ